Symplectic Geometry Seminar

Georgios Dimitroglou-Rizzell (Uppsala University)

Title: Relative Calabi-Yau structures and properties of the Augmentation Variety

Abstract:

The Legendrian contact homology dga can be endowed with a relative Calabi-Yau structure when the Legendrian is contained inside the boundary of a subcritical Weinstien manifold. We discuss the proof and geometric consequences for the augmentation variety, e.g. the property of being a holomorphic Lagrangian in certain favourable situations. Even in cases when there is no relative Calabi-Yau structure, e.g. for the knot contact homology dga of Ekholm-Etynre-Ng-Sullivan, we can get similar results by vanishing results of the Rabinowitz Floer homology for generic local systems on the conormal. This is joint work with N. Legout.